A Monte Carlo Method for the Normal Inverse Gaussian Option Valuation Model using an Inverse Gaussian Bridge

The normal inverse Gaussian process has been used to model both stock returns and interest rate processes. Although several numerical methods are available to compute, for instance, VaR and derivatives values, these are in a relatively undeveloped state compared to the techniques available in the Gaussian case. This paper shows how a Monte Carlo valuation method may be used with the NIG process, incorporating stratified sampling together with an inverse Gaussian bridge. The method is illustrated by pricing average rate options. We find the method is up to around 200 times faster than plain Monte Carlo. These efficiency gains are similar to those found in a related paper, Ribeiro and Webber (02) [20], which develops an analogous method for the variancegamma process. ∗Corresponding author. Claudia Ribeiro gratefully acknowledges the support of Fundação para a Ciência e a Tecnologia and Faculdade de Economia, Universidade do Porto. We are grateful for helpful discussions with participants at QMF Sydney 2002, and to Lynda McCarthy for detailed comments on the manuscript.